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Context. The precision of radial velocity (RV) measurements to detect indirectly planetary companions of nearby stars has improved to enable the discovery of extrasolar planets in the Neptune and Super-Earth mass range. Detections of extremely low mass planets, even as small as 1 Earth mass or below, in short-period orbits now appears conceivable in ongoing RV planet searches. Discoveries of these Earth-like planets by means of ground-based RV programs will help to determine the parameter eta(circle plus) the frequency of potentially habitable planets around other stars. Aims. In search of low-mass planetary companions we monitored Proxima Centauri (M5V) as part of our M dwarf program. In the absence of a significant detection, we use these data to demonstrate the general capability of the RV method in finding terrestrial planets. For late M dwarfs the classic liquid surface water habitable zone (HZ) is located close to the star, in which circumstances the RV method is most effective. We want to demonstrate that late M dwarfs are ideal targets for the search of terrestrial planets with the RV technique. Methods. Using the iodine cell technique we obtained differential RV measurements of Proxima Cen over a time span of 7 years with the UVES spectrograph at the ESO VLT. We determine upper limits to the masses of companions in circular orbits by means of numerical simulations. Results. The RV data of Proxima Cen have a total rms scatter of 3.1 m s(-1) and a period search does not reveal any significant signals. In contrast to our earlier results for Barnard's star, the RV results for the active M dwarf Proxima Cen are only weakly correlated with H(alpha) line index measurements. As a result of our companion limit calculations, we find that we successfully recover all test signals with RV amplitudes corresponding to planets with m sin i >= 2-3 M(circle plus) residing inside the HZ of Proxima Cen with a statistical significance of >99%. Over the same period range, we can recover 50% of the test planets with masses of m sin i >= 1.5-2.5 M(circle plus). Based on our simulations, we exclude the presence of any planet in a circular orbit with m sin i >= 1 M(Neptune) at separations of a <= 1 AU.